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6. Consider a circular tank of very large cross-section filled with water up to a level H. Water(density p) flows out through the bottom pipe of cross-sectional area Ao. Assume that the area of the tank, A₁ is much larger than A。 (A₁ >> A。). Neglect any viscous losses.

(a) Is the flow steady? Why or why not? (b) Can one use the quasi-steady assumption? Why or why not? (c) If the pipe is open to the atmosphere, the pressure at exit 3 is atmospheric pressure.What is the exit velocity V3? Obtain its expression in terms of the tube length h, and the water height in the tank H. Clearly identify which conservation law you are using. (d) Consider the shaded control volume CV2 within the pipe. Will the gage pressure at section 4 be zero, positive, or negative? Verify your answer by finding an expression for pressure at section 4 (P₁), which is at a distance x below the bottom of the tank. (e) If a pin hole is pierced through the pipe at section 4, what do you think will happen to the fluid? Will it ooze out through this pin hole? (f) What will be the gage pressure at the entrance to the pipe, i.e. when x = 0? Is this pressure same as hydrostatic pressure of √2gH? Why or why not?

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